you are correct that 4.3.5 is tethered jailbreak as well as OS5. However, with OS5, you can install Semi-tether from the big boss which I think it worth it if you want to go that way.
5.0.1 is coming out, so I am not sure if Apple still signs OS5, if they do then you have to move fast otherwise you won't be able to once they stop signing it.
By the way, if your phone have old bootrom, then you will have untethered jailbreak. So, run it with Idetector and see what you have.